/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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YES

Problem 1: 

(VAR x y z)
(RULES
+(minus(+(x,1)),1) -> minus(x)
+(minus(1),1) -> 0
+(0,y) -> y
+(x,+(y,z)) -> +(+(x,y),z)
+(x,minus(y)) -> minus(+(minus(x),y))
+(x,0) -> x
minus(minus(x)) -> x
minus(0) -> 0
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 +#(minus(+(x,1)),1) -> MINUS(x)
 +#(x,+(y,z)) -> +#(+(x,y),z)
 +#(x,+(y,z)) -> +#(x,y)
 +#(x,minus(y)) -> +#(minus(x),y)
 +#(x,minus(y)) -> MINUS(+(minus(x),y))
 +#(x,minus(y)) -> MINUS(x)
-> Rules:
 +(minus(+(x,1)),1) -> minus(x)
 +(minus(1),1) -> 0
 +(0,y) -> y
 +(x,+(y,z)) -> +(+(x,y),z)
 +(x,minus(y)) -> minus(+(minus(x),y))
 +(x,0) -> x
 minus(minus(x)) -> x
 minus(0) -> 0

Problem 1: 

SCC Processor:
-> Pairs:
 +#(minus(+(x,1)),1) -> MINUS(x)
 +#(x,+(y,z)) -> +#(+(x,y),z)
 +#(x,+(y,z)) -> +#(x,y)
 +#(x,minus(y)) -> +#(minus(x),y)
 +#(x,minus(y)) -> MINUS(+(minus(x),y))
 +#(x,minus(y)) -> MINUS(x)
-> Rules:
 +(minus(+(x,1)),1) -> minus(x)
 +(minus(1),1) -> 0
 +(0,y) -> y
 +(x,+(y,z)) -> +(+(x,y),z)
 +(x,minus(y)) -> minus(+(minus(x),y))
 +(x,0) -> x
 minus(minus(x)) -> x
 minus(0) -> 0
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 +#(x,+(y,z)) -> +#(+(x,y),z)
 +#(x,+(y,z)) -> +#(x,y)
 +#(x,minus(y)) -> +#(minus(x),y)
->->-> Rules:
 +(minus(+(x,1)),1) -> minus(x)
 +(minus(1),1) -> 0
 +(0,y) -> y
 +(x,+(y,z)) -> +(+(x,y),z)
 +(x,minus(y)) -> minus(+(minus(x),y))
 +(x,0) -> x
 minus(minus(x)) -> x
 minus(0) -> 0

Problem 1: 

Subterm Processor:
-> Pairs:
 +#(x,+(y,z)) -> +#(+(x,y),z)
 +#(x,+(y,z)) -> +#(x,y)
 +#(x,minus(y)) -> +#(minus(x),y)
-> Rules:
 +(minus(+(x,1)),1) -> minus(x)
 +(minus(1),1) -> 0
 +(0,y) -> y
 +(x,+(y,z)) -> +(+(x,y),z)
 +(x,minus(y)) -> minus(+(minus(x),y))
 +(x,0) -> x
 minus(minus(x)) -> x
 minus(0) -> 0
->Projection:
 pi(+#) = 2

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 +(minus(+(x,1)),1) -> minus(x)
 +(minus(1),1) -> 0
 +(0,y) -> y
 +(x,+(y,z)) -> +(+(x,y),z)
 +(x,minus(y)) -> minus(+(minus(x),y))
 +(x,0) -> x
 minus(minus(x)) -> x
 minus(0) -> 0
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.